Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot StdAge}{k+StdAge}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(StdAge\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FI A data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot StdAge} {k+StdAge} \right)\)

sub-model b: s form \(\left( \frac {A \cdot StdAge^s} {k^s+StdAge^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot StdAge^s} {k^s + StdAge^s} \right)\)

Note:

This analysis uses ALL available plot biomass data

which includes the following plot-based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9938     2556.7                                
## 2   9937     2541.4  1 15.341  59.985 1.049e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107909.7
## 2     2 107851.8
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.383270   0.101114  -3.790 0.000151 ***
## phi   0.052775   0.006569   8.034 1.05e-15 ***
## A   556.613146  34.179453  16.285  < 2e-16 ***
## k   245.186030  17.581092  13.946  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5057 on 9937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.762e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   9937     2541.4                          
## 2   9936     2540.9  1 0.48648  1.9024 0.1678
##   model      AIC
## 1     2 107851.8
## 2    2a 107851.9
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.383270   0.101114  -3.790 0.000151 ***
## phi   0.052775   0.006569   8.034 1.05e-15 ***
## A   556.613146  34.179453  16.285  < 2e-16 ***
## k   245.186030  17.581092  13.946  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5057 on 9937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.762e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 335 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 335 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 208 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1  30370      10683                         
## 2  30361      10682  9  1.207  0.3812 0.9447
##   model      AIC
## 1     1 316873.0
## 2     2 316790.5
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.003487   0.062219   0.056    0.955    
## phi  -0.005058   0.003123  -1.620    0.105    
## A   208.607545   4.439034  46.994   <2e-16 ***
## k    91.158802   2.492202  36.578   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5932 on 30361 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.498e-06
##   (30 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1  30361      10682                              
## 2  30360      10662  1  19.84  56.491 5.8e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 316790.5
## 2    2a 316736.1
## 3    2b 316780.2
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.023795   0.061696  -0.386     0.70    
## phi  -0.004728   0.003120  -1.516     0.13    
## A   230.695658   7.026466  32.832  < 2e-16 ***
## k   112.039694   5.271333  21.255  < 2e-16 ***
## p     0.013745   0.001721   7.985 1.45e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5926 on 30360 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.723e-06
##   (30 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 1184 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 1184 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 161 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1  11289     2126.3                           
## 2  11288     2126.3  1 0.027622  0.1466 0.7018
##   model      AIC
## 1     1 123755.5
## 2     2 123757.4
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.03093    0.07355  -0.421    0.674    
## A  494.44302   21.74831  22.735   <2e-16 ***
## k  158.15402    8.54362  18.511   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.434 on 11289 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.7e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: does not fit

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  11289     2126.3                          
## 2  11288     2126.2  1 0.10645  0.5652 0.4522
##   model      AIC
## 1     1 123755.5
## 2    1a 123756.9
## 3    1b       NA
## 4    1c       NA
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.03093    0.07355  -0.421    0.674    
## A  494.44302   21.74831  22.735   <2e-16 ***
## k  158.15402    8.54362  18.511   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.434 on 11289 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.7e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 364 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 364 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 97 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7909     2647.4                          
## 2   7908     2647.2  1 0.21999  0.6572 0.4176
##   model      AIC
## 1     1 85472.19
## 2     2 85473.53
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.2451     0.1104   -2.22   0.0264 *  
## A  528.2512    42.9834   12.29   <2e-16 ***
## k  242.8753    22.7556   10.67   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5786 on 7909 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.799e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   7909     2647.4                              
## 2   7908     2644.2  1 3.1482  9.4151 0.002159 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85472.19
## 2    1a 85464.77
## 3    1b       NA
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  -0.229136   0.111317  -2.058   0.0396 *  
## A  449.068734  41.427170  10.840  < 2e-16 ***
## k  189.508155  23.529869   8.054 9.19e-16 ***
## p   -0.008452   0.003651  -2.315   0.0206 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5783 on 7908 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.275e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 268 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 268 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 61 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13436     2603.2                                
## 2  13435     2600.1  1 3.1828  16.446 5.034e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 140769.3
## 2     2 140754.9
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.059184   0.072709   0.814    0.416    
## phi  -0.018594   0.004521  -4.113 3.93e-05 ***
## A   238.276645   6.455550  36.910  < 2e-16 ***
## k    73.287908   2.872621  25.513  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4399 on 13435 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.823e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1  13435     2600.1                               
## 2  13434     2600.1  1  0.0004   0.0021 0.9635    
## 3  13434     2593.9  0  0.0000                    
## 4  13433     2571.9  1 21.9779 114.7902 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 140754.9
## 2    2a 140756.9
## 3    2b 140724.9
## 4    2c 140612.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.082410   0.073052   1.128 0.259296    
## phi  -0.016545   0.004501  -3.675 0.000238 ***
## A   144.478610   3.756822  38.458  < 2e-16 ***
## k    38.479465   1.013132  37.981  < 2e-16 ***
## p     0.145366   0.012293  11.825  < 2e-16 ***
## s     2.115570   0.105329  20.085  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4376 on 13433 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.699e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 372 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 372 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 44 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1  19932     6444.3                            
## 2  19931     6442.9  1 1.4098  4.3612 0.03678 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 217634.0
## 2     2 217631.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.635113   0.075632   8.397   <2e-16 ***
## phi  -0.008778   0.004210  -2.085   0.0371 *  
## A   273.716406   6.200726  44.143   <2e-16 ***
## k    66.637249   1.817470  36.665   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5686 on 19931 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.649e-06
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  19931     6442.9                                 
## 2  19930     6390.5  1  52.413  163.46 < 2.2e-16 ***
## 3  19930     6434.4  0   0.000                      
## 4  19929     6321.2  1 113.247  357.04 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 217631.6
## 2    2a 217470.8
## 3    2b 217607.5
## 4    2c 217255.6
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.696041   0.076247   9.129   <2e-16 ***
## phi  -0.009557   0.004162  -2.296   0.0217 *  
## A   174.697261   4.714684  37.054   <2e-16 ***
## k    33.390061   1.183674  28.209   <2e-16 ***
## p     0.070684   0.003851  18.354   <2e-16 ***
## s     1.626479   0.045572  35.690   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5632 on 19929 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.992e-06
##   (26 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 629 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 629 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 78 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  20858     9688.4                                
## 2  20855     9677.1  3 11.326  8.1366 2.065e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 232500.8
## 2     2 232460.1
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.23827    0.07490   3.181  0.00147 ** 
## phi   0.01426    0.00516   2.763  0.00574 ** 
## A   300.75555    8.24620  36.472  < 2e-16 ***
## k    76.56971    2.56518  29.850  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6812 on 20855 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.192e-07
##   (60 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  20855     9677.1                                 
## 2  20854     9613.9  1  63.196  137.08 < 2.2e-16 ***
## 3  20854     9664.0  0   0.000                      
## 4  20853     9549.8  1 114.204  249.38 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 232460.1
## 2    2a 232325.5
## 3    2b 232434.0
## 4    2c 232188.0
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  2.429e-01  7.416e-02   3.275  0.00106 ** 
## phi 1.507e-02  5.119e-03   2.944  0.00324 ** 
## A   1.943e+02  6.621e+00  29.353  < 2e-16 ***
## k   3.837e+01  1.793e+00  21.402  < 2e-16 ***
## p   6.184e-02  4.309e-03  14.349  < 2e-16 ***
## s   1.554e+00  5.041e-02  30.828  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6767 on 20853 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.006e-06
##   (60 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 810 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 810 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 101 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   2186     817.40                            
## 2   2185     815.82  1 1.5791  4.2294 0.03985 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24934.44
## 2     2 24932.20
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.12226    0.23290  -0.525   0.5997    
## phi   0.03788    0.01859   2.037   0.0417 *  
## A   531.80592   74.36941   7.151 1.17e-12 ***
## k   161.97411   27.41420   5.908 4.00e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.611 on 2185 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.058e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   2185     815.82                              
## 2   2184     814.69  1 1.1257  3.0176 0.082505 . 
## 3   2184     815.53  0 0.0000                    
## 4   2183     813.00  1 2.5343  6.8049 0.009153 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 24932.20
## 2    2a 24931.18
## 3    2b 24933.42
## 4    2c 24928.61
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.13384    0.23173  -0.578   0.5636    
## phi   0.03911    0.01856   2.107   0.0352 *  
## A   315.56482   79.16136   3.986 6.93e-05 ***
## k    72.27038   23.67493   3.053   0.0023 ** 
## p     0.04870    0.02473   1.969   0.0490 *  
## s     1.45175    0.24454   5.937 3.38e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6103 on 2183 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.444e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89517, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.499, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 62 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 62 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 80 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    242     61.785                         
## 2    241     61.380  1 0.4051  1.5906 0.2085
##   model      AIC
## 1     1 3066.116
## 2     2 3066.504
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)   
## ge   -0.5420     0.4969  -1.091  0.27643   
## A  1647.4704   530.1361   3.108  0.00211 **
## k   324.5869   108.1129   3.002  0.00296 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5053 on 242 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 3.697e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1    242     61.785                           
## 2    241     60.734  1 1.0513  4.1715 0.0422 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3066.116
## 2    1a 3063.912
## 3    1b       NA
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.61613    0.47586  -1.295 0.196637    
## A  1260.29437  377.58223   3.338 0.000978 ***
## k   199.37313   76.59181   2.603 0.009813 ** 
## p    -0.02135    0.01610  -1.326 0.186046    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.502 on 241 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 6.549e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9639, p-value = 7.59e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.2638, p-value = 0.001099
## alternative hypothesis: two.sided

predict and plot

plotting 2

## Warning: Removed 1 rows containing missing values (geom_segment).

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   2781     760.98                           
## 2   2780     760.95  1 0.034127  0.1247  0.724
##   model      AIC
## 1     1 29399.95
## 2     2 29401.83
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3455     0.1580  -2.187   0.0289 *  
## A  303.2515    24.8271  12.215   <2e-16 ***
## k  114.1674    11.9374   9.564   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5231 on 2781 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.755e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   2781     760.98                             
## 2   2780     760.17  1 0.81064  2.9646 0.08522 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29399.95
## 2    1a 29398.99
## 3    1b 29390.81
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + 
##     STDAGE^s))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3165     0.1596  -1.983   0.0475 *  
## A  191.1468    18.4763  10.345  < 2e-16 ***
## k   50.8835     7.0584   7.209 7.23e-13 ***
## s    1.3703     0.1031  13.288  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5222 on 2780 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.049e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96263, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -24.432, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 98 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 98 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 97 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1282     497.71                           
## 2   1281     497.68  1 0.026566  0.0684 0.7938
##   model      AIC
## 1     1 13108.71
## 2     2 13110.64
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.4374     0.2635  -1.660   0.0971 .  
## A  220.2286    25.1890   8.743  < 2e-16 ***
## k   82.2162    11.9149   6.900 8.14e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6231 on 1282 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.21e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1282     497.71                           
## 2   1281     497.69  1 0.022344  0.0575 0.8105
##   model      AIC
## 1     1 13108.71
## 2    1a 13110.66
## 3    1b 13102.40
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + 
##     STDAGE^s))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.4803     0.2575  -1.865   0.0624 .  
## A  134.9472    16.4694   8.194 6.07e-16 ***
## k   33.0748     5.9587   5.551 3.46e-08 ***
## s    1.4034     0.1365  10.279  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6213 on 1281 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 9.017e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94897, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.208, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1     52     8.7701                           
## 2     51     8.7310  1 0.039108  0.2284 0.6347
##   model      AIC
## 1     1 726.1735
## 2     2 727.9277
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.2077     1.1507   0.180   0.8575  
## A  905.7823   342.5092   2.645   0.0108 *
## k  148.4811    65.0617   2.282   0.0266 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4107 on 52 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.161e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_261,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1     52     8.7701                            
## 2     51     8.7682  1 0.0018825  0.0109 0.9171
##   model      AIC
## 1     1 726.1735
## 2    1a 728.1617
## 3    1b 728.1731
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.2077     1.1507   0.180   0.8575  
## A  905.7823   342.5092   2.645   0.0108 *
## k  148.4811    65.0617   2.282   0.0266 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4107 on 52 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.161e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits

  • add s model: fits

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94289, p-value = 0.01129
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.38722, p-value = 0.6986
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 6 rows containing missing values (geom_point).
## Warning: Removed 332 row(s) containing missing values (geom_path).

plotting 2

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_262.' not found

summary

  • simple model: does not fit
  • phi model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    426     98.090                            
## 2    425     97.026  1 1.0635  4.6584 0.03146 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5410.292
## 2     2 5407.615
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.29301    0.68606   1.885   0.0602 .  
## phi   -0.08221    0.03786  -2.171   0.0305 *  
## A   1049.16808  209.39393   5.010 7.98e-07 ***
## k    224.28333   45.52407   4.927 1.20e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4778 on 425 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.113e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_263,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    425     97.026                          
## 2    424     96.827  1 0.19956  0.8739 0.3504
##   model      AIC
## 1     2 5407.615
## 2    2a 5408.732
## 3    2b 5404.762
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   1.558e+00  7.516e-01   2.073   0.0388 *  
## phi -6.898e-02  3.817e-02  -1.807   0.0715 .  
## A    5.777e+03  1.342e+04   0.430   0.6672    
## k    4.975e+03  1.915e+04   0.260   0.7952    
## s    7.450e-01  1.037e-01   7.185 3.04e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4757 on 424 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 2.064e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97891, p-value = 6.856e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8867, p-value = 3.94e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    503     197.73                            
## 2    502     196.55  1 1.1824  3.0198 0.08287 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5500.917
## 2     2 5499.883
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.74878    0.45224  -1.656 0.098404 .  
## phi  -0.06604    0.04231  -1.561 0.119148    
## A   198.37376   34.24510   5.793 1.22e-08 ***
## k   126.91926   32.37995   3.920 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6257 on 502 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.528e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    502     196.55                          
## 2    501     196.12  1 0.42914  1.0963 0.2956
##   model      AIC
## 1     2 5499.883
## 2    2a 5500.777
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.74878    0.45224  -1.656 0.098404 .  
## phi  -0.06604    0.04231  -1.561 0.119148    
## A   198.37376   34.24510   5.793 1.22e-08 ***
## k   126.91926   32.37995   3.920 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6257 on 502 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.528e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89169, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5305, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 18 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 18 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 141 row(s) containing missing values (geom_path).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1     13     3559.6                         
## 2     12     3499.8  1 59.729  0.2048  0.659
##   model      AIC
## 1     1 139.8829
## 2     2 141.6121
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## ge   -1.737      1.176  -1.477    0.163
## A   119.386    102.105   1.169    0.263
## k   101.084    115.067   0.878    0.396
## 
## Residual standard error: 16.55 on 13 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.662e-06

summary

  • simple model: fits
  • phi model: fits

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

## Error in nls(f_1, data = P_321, start = c(ge = ge.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     1       NA
## 2     2 233.4009
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -5.13892    0.64567  -7.959 3.91e-07 ***
## phi   0.51139    0.06174   8.283 2.27e-07 ***
## A   411.66201  306.73023   1.342    0.197    
## k    25.60602   68.48660   0.374    0.713    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8705 on 17 degrees of freedom
## 
## Number of iterations to convergence: 31 
## Achieved convergence tolerance: 7.859e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_321,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_321,  : 
##   singular gradient
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1     17     12.883                          
## 2     16     12.691  1 0.19219  0.2423 0.6292
##   model      AIC
## 1     2 233.4009
## 2    2a 235.0852
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -5.13892    0.64567  -7.959 3.91e-07 ***
## phi   0.51139    0.06174   8.283 2.27e-07 ***
## A   411.66201  306.73023   1.342    0.197    
## k    25.60602   68.48660   0.374    0.713    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8705 on 17 degrees of freedom
## 
## Number of iterations to convergence: 31 
## Achieved convergence tolerance: 7.859e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.80767, p-value = 0.0008613
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.79305, p-value = 0.4277
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 21 row(s) containing missing values (geom_path).

plotting 2

## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_pointrange).
## Warning: Removed 15 rows containing missing values (geom_segment).

322 - American Semidesert and Desert

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1      5     5487.1                         
## 2      4     5479.9  1 7.2366  0.0053 0.9456
##   model      AIC
## 1     1 82.94879
## 2     2 84.93823
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge    3.598     13.618   0.264   0.8022  
## A    20.616     37.917   0.544   0.6100  
## k   -78.208     32.792  -2.385   0.0628 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 33.13 on 5 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.894e-06

summary

  • simple model: fits
  • phi model: fits

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    749     502.27                         
## 2    748     500.96  1 1.3185  1.9687  0.161
##   model      AIC
## 1     1 7643.027
## 2     2 7643.050
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3773     0.5245  -0.719    0.472    
## A  111.0018    18.8722   5.882 6.12e-09 ***
## k   78.2492    16.6590   4.697 3.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8189 on 749 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.308e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    749     502.27                                
## 2    748     501.49  1  0.786  1.1724    0.2793    
## 3    748     502.02  0  0.000                      
## 4    747     489.77  1 12.249 18.6829 1.753e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7643.027
## 2    1a 7643.849
## 3    1b 7644.646
## 4    1c 7628.070
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge -0.15646    0.56610  -0.276 0.782335    
## A  58.03452    7.69556   7.541 1.35e-13 ***
## k  33.19091    3.02797  10.961  < 2e-16 ***
## p   0.18739    0.03023   6.199 9.39e-10 ***
## s   3.92007    1.13605   3.451 0.000591 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8097 on 747 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.363e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86401, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.021, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 28 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 28 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 60 row(s) containing missing values (geom_path).

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    319     225.08                          
## 2    318     224.66  1 0.41885  0.5929 0.4419
##   model      AIC
## 1     1 3495.454
## 2     2 3496.854
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.2726     0.8399  -0.325   0.7457  
## A  221.7114   101.3257   2.188   0.0294 *
## k  111.7604    64.6879   1.728   0.0850 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.84 on 319 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.338e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    319     225.08                         
## 2    317     222.68  2 2.4005  1.7086 0.1828
##   model      AIC
## 1     1 3495.454
## 2    1a       NA
## 3    1b       NA
## 4    1c 3496.001
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.2726     0.8399  -0.325   0.7457  
## A  221.7114   101.3257   2.188   0.0294 *
## k  111.7604    64.6879   1.728   0.0850 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.84 on 319 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.338e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84817, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.635, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 8 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 15 row(s) containing missing values (geom_path).

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    143     47.059                          
## 2    142     47.037  1 0.02145  0.0648 0.7995
##   model      AIC
## 1     1 1568.704
## 2     2 1570.637
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge    1.749      1.660   1.054  0.29378   
## A   148.616     56.564   2.627  0.00954 **
## k   126.961     52.086   2.438  0.01602 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5737 on 143 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.06e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    143     47.059                          
## 2    142     46.698  1 0.36055  1.0964 0.2968
##   model      AIC
## 1     1 1568.704
## 2    1a 1569.581
## 3    1b 1570.581
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge    1.749      1.660   1.054  0.29378   
## A   148.616     56.564   2.627  0.00954 **
## k   126.961     52.086   2.438  0.01602 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5737 on 143 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.06e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97269, p-value = 0.005155
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.0983, p-value = 4.161e-05
## alternative hypothesis: two.sided

predict and plot

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    316     283.29                         
## 2    315     282.17  1 1.1229  1.2536 0.2637
##   model      AIC
## 1     1 3436.751
## 2     2 3437.484
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  0.04513    1.12715   0.040 0.968089    
## A  91.27600   27.15012   3.362 0.000869 ***
## k  60.03226   22.50994   2.667 0.008049 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9468 on 316 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.267e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    316     283.29                         
## 2    315     281.67  1 1.6192  1.8108 0.1794
##   model      AIC
## 1     1 3436.751
## 2    1a 3436.922
## 3    1b 3437.837
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  0.04513    1.12715   0.040 0.968089    
## A  91.27600   27.15012   3.362 0.000869 ***
## k  60.03226   22.50994   2.667 0.008049 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9468 on 316 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.267e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88033, p-value = 4.504e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.7423, p-value = 9.342e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 12 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 12 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 95 row(s) containing missing values (geom_path).

plotting 2

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).

411 - Everglades

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    166     71.634                                
## 2    165     67.027  1 4.6065   11.34 0.0009441 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1787.685
## 2     2 1778.452
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    -1.7989     0.4433  -4.058 7.62e-05 ***
## phi   -0.3428     0.1230  -2.786  0.00596 ** 
## A   1605.1761  3041.3144   0.528  0.59835    
## k    764.0349  1516.4489   0.504  0.61505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6374 on 165 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.365e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_411,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_411,  : 
##   singular gradient
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_411,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     2 1778.452
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    -1.7989     0.4433  -4.058 7.62e-05 ***
## phi   -0.3428     0.1230  -2.786  0.00596 ** 
## A   1605.1761  3041.3144   0.528  0.59835    
## k    764.0349  1516.4489   0.504  0.61505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6374 on 165 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.365e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97702, p-value = 0.006624
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.826, p-value = 1.393e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10057     2001.3                                
## 2  10056     1994.5  1 6.8491  34.532 4.325e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107037.0
## 2     2 107004.5
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  8.733e-02  9.286e-02    0.94    0.347    
## phi 3.115e-02  5.504e-03    5.66 1.56e-08 ***
## A   4.790e+02  2.391e+01   20.03  < 2e-16 ***
## k   2.205e+02  1.280e+01   17.23  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4454 on 10056 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.401e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10056     1994.5                                
## 2  10055     1987.0  1 7.4779  37.841 7.967e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 107004.5
## 2    2a 106968.7
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.054423   0.091634   0.594    0.553    
## phi   0.030372   0.005481   5.541 3.08e-08 ***
## A   377.503856  20.268188  18.625  < 2e-16 ***
## k   144.875032  12.158229  11.916  < 2e-16 ***
## p    -0.021206   0.004829  -4.391 1.14e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4445 on 10055 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.957e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 346 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 346 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 106 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13160     2210.7                                
## 2  13159     2191.1  1 19.627  117.87 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 145414.7
## 2     2 145299.3
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.548961   0.071191   7.711 1.34e-14 ***
## phi  -0.038971   0.003549 -10.980  < 2e-16 ***
## A   271.111248   6.089184  44.523  < 2e-16 ***
## k    63.850565   2.100846  30.393  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4081 on 13159 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.803e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1  13159     2191.1                              
## 2  13158     2191.0  1  0.052   0.3099 0.5777    
## 3  13158     2178.8  0  0.000                    
## 4  13157     2146.2  1 32.590 199.7893 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 145299.3
## 2    2a 145301.0
## 3    2b 145227.4
## 4    2c 145031.0
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.642941   0.073275   8.774   <2e-16 ***
## phi  -0.037296   0.003508 -10.631   <2e-16 ***
## A   170.328853   3.502018  48.637   <2e-16 ***
## k    37.150549   0.741208  50.122   <2e-16 ***
## p     0.165317   0.009961  16.596   <2e-16 ***
## s     2.342576   0.099384  23.571   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4039 on 13157 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.84e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 472 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 472 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 67 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1243     169.25                                
## 2   1242     166.62  1 2.6234  19.555 1.063e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 12649.64
## 2     2 12632.18
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.52664    0.15034  -3.503 0.000476 ***
## phi   0.06689    0.01592   4.202 2.84e-05 ***
## A   271.29836   24.43298  11.104  < 2e-16 ***
## k    83.42650   11.61984   7.180 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3663 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.432e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1242     166.62                           
## 2   1241     166.59  1 0.035854  0.2671 0.6054
## 3   1241     166.55  0 0.000000               
## 4   1240     166.53  1 0.028854  0.2149 0.6431
##   model      AIC
## 1     2 12632.18
## 2    2a 12633.91
## 3    2b 12633.65
## 4    2c 12635.43
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.52664    0.15034  -3.503 0.000476 ***
## phi   0.06689    0.01592   4.202 2.84e-05 ***
## A   271.29836   24.43298  11.104  < 2e-16 ***
## k    83.42650   11.61984   7.180 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3663 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.432e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97257, p-value = 1.24e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.49, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 23 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 23 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 20 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   1484     342.22                             
## 2   1483     341.30  1 0.92221  4.0072 0.04549 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15286.15
## 2     2 15284.13
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.15481    0.24948   0.621   0.5350    
## phi   0.03631    0.01849   1.964   0.0497 *  
## A   316.03672   38.38330   8.234 3.94e-16 ***
## k   142.92057   21.27357   6.718 2.61e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1483 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.777e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1483     341.30                           
## 2   1482     341.24  1 0.055697  0.2419 0.6229
## 3   1482     341.20  0 0.000000               
## 4   1481     341.19  1 0.008313  0.0361 0.8494
##   model      AIC
## 1     2 15284.13
## 2    2a 15285.89
## 3    2b 15285.71
## 4    2c 15287.68
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.15481    0.24948   0.621   0.5350    
## phi   0.03631    0.01849   1.964   0.0497 *  
## A   316.03672   38.38330   8.234 3.94e-16 ***
## k   142.92057   21.27357   6.718 2.61e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1483 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.777e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96927, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.614, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 39 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 39 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 36 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7934     4843.9                          
## 2   7933     4843.0  1 0.86271  1.4131 0.2346
##   model      AIC
## 1     1 105723.9
## 2     2 105724.4
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.02465    0.16455    0.15    0.881    
## A  780.98344   41.40997   18.86   <2e-16 ***
## k  223.08680   12.70480   17.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7814 on 7934 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.343e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7934     4843.9                                 
## 2   7933     4825.5  1 18.4033 30.2546 3.907e-08 ***
## 3   7932     4825.3  1  0.1519  0.2497    0.6173    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 105723.9
## 2    1a 105695.6
## 3    1b       NA
## 4    1c 105697.4
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   0.008305   0.163098   0.051    0.959    
## A  682.531690  36.459330  18.720  < 2e-16 ***
## k  159.113169  12.652352  12.576  < 2e-16 ***
## p   -0.033932   0.007527  -4.508 6.63e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7799 on 7933 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.717e-07
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 327 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 327 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 633 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4571     2296.8                                
## 2   4570     2264.8  1 32.069  64.711 1.096e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 57841.68
## 2     2 57779.37
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    2.35377    0.46352   5.078 3.96e-07 ***
## phi   0.10652    0.01124   9.476  < 2e-16 ***
## A   355.35507   27.88660  12.743  < 2e-16 ***
## k   148.96824   12.01719  12.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.704 on 4570 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.649e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   4570     2264.8                          
## 2   4569     2264.4  1 0.33289  0.6717 0.4125
## 3   4569     2264.7  0 0.00000               
## 4   4568     2264.2  1 0.49094  0.9905 0.3197
##   model      AIC
## 1     2 57779.37
## 2    2a 57780.69
## 3    2b 57781.25
## 4    2c 57782.26
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    2.35377    0.46352   5.078 3.96e-07 ***
## phi   0.10652    0.01124   9.476  < 2e-16 ***
## A   355.35507   27.88660  12.743  < 2e-16 ***
## k   148.96824   12.01719  12.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.704 on 4570 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.649e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91632, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -25.825, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 206 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 206 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 727 row(s) containing missing values (geom_path).

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Error in nls(f_1, data = P_M262, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Warning: Unknown or uninitialised column: `nls_weights.2`.
##   model      AIC
## 1     1       NA
## 2     2 615.3221
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   -1.8417     0.8477  -2.172  0.03459 *  
## phi  -0.3664     0.2019  -1.814  0.07561 .  
## A    84.9819    25.1232   3.383  0.00140 ** 
## k   -22.9322     5.4606  -4.200  0.00011 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 68.33 on 50 degrees of freedom
## 
## Number of iterations to convergence: 23 
## Achieved convergence tolerance: 6.694e-06

summary

  • simple model: does not fit
  • phi model: fits

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    909     285.04                          
## 2    908     284.23  1 0.80661  2.5768 0.1088
##   model      AIC
## 1     1 9546.030
## 2     2 9545.445
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.69254    0.30491  -2.271  0.02336 *  
## phi   0.03350    0.01897   1.765  0.07785 .  
## A   414.52469  104.07497   3.983 7.35e-05 ***
## k   302.50777   94.96416   3.185  0.00149 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5595 on 908 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.596e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    908     284.23                            
## 2    907     284.23  1 0.0031111  0.0099 0.9207
##   model      AIC
## 1     2 9545.445
## 2    2a 9547.435
## 3    2b       NA
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.69254    0.30491  -2.271  0.02336 *  
## phi   0.03350    0.01897   1.765  0.07785 .  
## A   414.52469  104.07497   3.983 7.35e-05 ***
## k   302.50777   94.96416   3.185  0.00149 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5595 on 908 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.596e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95495, p-value = 4.137e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.9791, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 36 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 36 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 133 row(s) containing missing values (geom_path).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   5206     1817.9                           
## 2   5205     1817.9  1 0.018864   0.054 0.8162
##   model      AIC
## 1     1 54576.09
## 2     2 54578.04
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.9551     0.0997   -9.58   <2e-16 ***
## A  284.9903    14.4710   19.69   <2e-16 ***
## k  167.7136    11.2787   14.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5909 on 5206 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.581e-07
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5206     1817.9                                 
## 2   5205     1811.1  1  6.7617  19.433 1.063e-05 ***
## 3   5205     1816.6  0  0.0000                      
## 4   5204     1791.6  1 24.9337  72.423 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 54576.09
## 2    1a 54558.68
## 3    1b 54574.30
## 4    1c 54504.31
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.98193    0.09797  -10.02   <2e-16 ***
## A  170.75202    8.45560   20.19   <2e-16 ***
## k   83.50593    4.15254   20.11   <2e-16 ***
## p    0.13634    0.01240   11.00   <2e-16 ***
## s    2.13892    0.15850   13.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5868 on 5204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.175e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 195 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 195 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 511 row(s) containing missing values (geom_path).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6772     3204.3                                
## 2   6771     3190.9  1 13.434  28.508 9.634e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 73901.46
## 2     2 73875.00
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.504e-01  1.856e-01   1.888   0.0591 .  
## phi 5.170e-02  9.073e-03   5.698 1.26e-08 ***
## A   2.253e+02  1.175e+01  19.184  < 2e-16 ***
## k   1.453e+02  8.485e+00  17.129  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6865 on 6771 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.071e-06
##   (5 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   6771     3190.9                            
## 2   6770     3188.6  1 2.2882  4.8583 0.02755 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 73875.00
## 2    2a 73872.14
## 3    2b 73873.04
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.328e-01  1.846e-01   1.803   0.0715 .  
## phi 5.299e-02  9.054e-03   5.852 5.08e-09 ***
## A   2.401e+02  1.620e+01  14.816  < 2e-16 ***
## k   1.656e+02  1.637e+01  10.115  < 2e-16 ***
## p   8.549e-03  3.898e-03   2.193   0.0283 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6863 on 6770 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.081e-06
##   (5 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 259 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 259 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 274 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4434     1963.5                                
## 2   4433     1953.8  1 9.7019  22.012 2.791e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 49716.85
## 2     2 49696.87
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.31327    0.23183   1.351    0.177    
## phi   0.05343    0.01098   4.867 1.17e-06 ***
## A   353.28995   25.05730  14.099  < 2e-16 ***
## k   185.81962   13.58745  13.676  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6639 on 4433 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.849e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1   4433     1953.8                            
## 2   4432     1953.8  1 0.0054658  0.0124 0.9113
##   model      AIC
## 1     2 49696.87
## 2    2a 49698.86
## 3    2b 49654.37
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.31425    0.23062   1.363    0.173    
## phi   0.04752    0.01103   4.309 1.67e-05 ***
## A   227.37954   17.22538  13.200  < 2e-16 ***
## k    82.08926    8.13709  10.088  < 2e-16 ***
## s     1.29097    0.04711  27.405  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6606 on 4432 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.711e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93128, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -19.5, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 171 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 171 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 200 row(s) containing missing values (geom_path).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    712     278.71                         
## 2    711     277.68  1 1.0259  2.6267 0.1055
##   model      AIC
## 1     1 7183.953
## 2     2 7183.316
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.26900    0.39205  -0.686    0.493    
## phi   0.03120    0.01943   1.606    0.109    
## A   119.13429   17.23489   6.912 1.06e-11 ***
## k    74.13118   16.35263   4.533 6.81e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6249 on 711 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.953e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_M334,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    711     277.68                          
## 2    710     277.10  1 0.57808  1.4812  0.224
##   model      AIC
## 1     2 7183.316
## 2    2a 7183.826
## 3    2b 7183.207
## 4    2c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge  -3.571e-01  3.791e-01  -0.942  0.34650   
## phi  3.184e-02  1.944e-02   1.638  0.10194   
## A    6.329e+02  2.290e+03   0.276  0.78232   
## k    3.062e+03  2.373e+04   0.129  0.89734   
## s    6.114e-01  2.046e-01   2.988  0.00291 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6245 on 710 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 4.116e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95815, p-value = 2.115e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5121, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 20 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 20 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 126 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    488     179.57                            
## 2    487     179.57  1 0.0011376  0.0031 0.9557
##   model      AIC
## 1     1 4981.344
## 2     2 4983.341
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.3411     0.2633  -5.094 5.03e-07 ***
## A  244.7652    37.7876   6.477 2.28e-10 ***
## k  169.2618    36.5092   4.636 4.56e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6066 on 488 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.218e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    488     179.57                          
## 2    487     179.29  1 0.28503  0.7742 0.3793
##   model      AIC
## 1     1 4981.344
## 2    1a 4982.564
## 3    1b 4983.315
## 4    1c       NA
## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.3411     0.2633  -5.094 5.03e-07 ***
## A  244.7652    37.7876   6.477 2.28e-10 ***
## k  169.2618    36.5092   4.636 4.56e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6066 on 488 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.218e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91761, p-value = 1.013e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.3092, p-value = 2.805e-10
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 21 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 21 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 226 row(s) containing missing values (geom_path).

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2a
221 Eastern Broadleaf Forest 1
222 Midwest Broadleaf Forest 1a
223 Central Interior Broadleaf Forest 2c
231 Southeastern Mixed Forest 2c
232 Outer Coastal Plain Mixed Forest 2c
234 Lower Mississippi Riverine Forest 2c
242 Pacific Lowland Mixed Forest 1a
251 Prairie Parkland (Temperate) 1b
255 Prairie Parkland (Subtropical) 1b
261 California Coastal Chaparral Forest and Shrub 1
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 2b
313 Colorado Plateau Semi-Desert 2
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert 2
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 1c
332 Great Plains Steppe 1
341 Intermountain Semi-Desert and Desert 1
342 Intermountain Semi-Desert 1
411 Everglades 2
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2a
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 1a
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 1c
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2b
M334 Black Hills Coniferous Forest 2b
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 1

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.2.5 ge.97.5 phi phi.2.5 phi.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 9943 3257 -0.3834057 -0.5817956 -0.1850157 0.0527788 0.0398888 0.0656689 556.3410 489.33083 623.3512 245.01954 210.55308 279.48600
212 Laurentian Mixed Forest east 30395 11945 -0.0237945 -0.1447212 0.0971322 -0.0047284 -0.0108434 0.0013866 230.6957 216.92349 244.4678 112.03969 101.70766 122.37173
221 Eastern Broadleaf Forest east 11294 4269 -0.0309342 -0.1750956 0.1132271 NA NA NA 494.4430 451.81253 537.0735 158.15402 141.40703 174.90101
222 Midwest Broadleaf Forest east 7913 3189 -0.2294793 -0.4476705 -0.0112880 NA NA NA 449.2132 367.93867 530.4877 189.57101 143.41110 235.73091
223 Central Interior Broadleaf Forest east 13446 4895 0.0824103 -0.0607820 0.2256026 -0.0165446 -0.0253681 -0.0077211 144.4786 137.11471 151.8425 38.47946 36.49358 40.46535
231 Southeastern Mixed Forest east 19961 7904 0.6960411 0.5465897 0.8454924 -0.0095572 -0.0177145 -0.0013999 174.6973 165.45609 183.9384 33.39006 31.06996 35.71016
232 Outer Coastal Plain Mixed Forest east 20919 9046 0.2428901 0.0975352 0.3882451 0.0150706 0.0050373 0.0251038 194.3326 181.35574 207.3094 38.36687 34.85302 41.88072
234 Lower Mississippi Riverine Forest east 2190 937 -0.1399492 -0.5944799 0.3145815 0.0410041 0.0045890 0.0774191 348.3264 143.08326 553.5696 82.45246 16.59542 148.30950
242 Pacific Lowland Mixed Forest pacific 246 172 -0.6957324 -1.6314706 0.2400058 NA NA NA 1353.4349 571.98418 2134.8855 221.67673 64.97612 378.37734
251 Prairie Parkland (Temperate) east 2787 1036 -0.3161358 -0.6290206 -0.0032510 NA NA NA 191.1599 154.94041 227.3793 50.89257 37.05698 64.72816
255 Prairie Parkland (Subtropical) pacific 1288 659 -0.4790572 -1.0318945 0.0737801 NA NA NA 298.2108 143.99447 452.4271 144.23738 36.02426 252.45051
261 California Coastal Chaparral Forest and Shrub pacific 56 34 -0.5508826 -2.3004831 1.1987180 NA NA NA 1177.4191 288.14609 2066.6921 197.25699 18.00118 376.51280
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 430 274 1.9228927 0.2200672 3.6257182 -0.0784330 -0.1556438 -0.0012221 779.6760 425.18039 1134.1716 163.27164 66.66000 259.88327
313 Colorado Plateau Semi-Desert interior west 508 312 -0.6736937 -1.4831964 0.1358090 NA NA NA 232.3414 151.53170 313.1510 136.52195 68.30490 204.73900
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 16 12 NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 22 14 NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 8 5 NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 753 473 -0.2920439 -1.3626069 0.7785191 NA NA NA 114.0569 74.43472 153.6791 84.70443 48.66040 120.74847
332 Great Plains Steppe interior west 324 152 -0.1183436 -1.9004767 1.6637894 NA NA NA 252.7441 -10.39279 515.8811 141.41701 -36.96816 319.80218
341 Intermountain Semi-Desert and Desert interior west 147 93 1.7454617 -1.8836762 5.3745996 NA NA NA 108.4568 22.21585 194.6977 79.58625 35.48962 123.68288
342 Intermountain Semi-Desert interior west 320 222 -0.0838740 -2.1131437 1.9453958 -0.1058914 -0.2317662 0.0199834 102.3313 41.44304 163.2195 80.40459 22.18500 138.62418
411 Everglades east 170 86 -1.5444141 -2.6052778 -0.4835504 -0.3501231 -0.5830968 -0.1171495 2528.1928 -13882.56878 18938.9545 1394.40105 -7881.08453 10669.88662
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 10063 3398 0.0617597 -0.1196180 0.2431375 0.0305975 0.0197735 0.0414214 402.0594 355.74312 448.3758 162.86850 134.37891 191.35810
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 13165 4970 0.6429412 0.4993110 0.7865714 -0.0372962 -0.0441726 -0.0304197 170.3289 163.46439 177.1933 37.15055 35.69767 38.60342
M223 Ozark Broadleaf Forest Meadow east 1248 392 -0.5479965 -0.8405470 -0.2554461 0.0676987 0.0363913 0.0990061 270.6138 223.52988 317.6977 82.46401 60.22919 104.69883
M231 Ouachita Mixed Forest east 1488 574 0.1446793 -0.3426034 0.6319619 0.0363254 0.0000474 0.0726033 318.2463 241.96078 394.5318 143.84477 101.57838 186.11117
M242 Cascade Mixed Forest pacific 7940 4900 0.0100745 -0.3105141 0.3306632 NA NA NA 599.9211 526.77743 673.0648 132.06763 108.12799 156.00727
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 4575 2761 2.3135410 1.4133041 3.2137780 0.1062596 0.0841257 0.1283935 359.8072 304.99899 414.6153 150.63590 126.98372 174.28807
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 54 38 NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 913 563 -0.6563364 -1.2660055 -0.0466674 0.0345127 -0.0025632 0.0715886 414.3138 208.62715 620.0005 304.46546 115.80800 493.12291
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 5236 3514 -0.9814603 -1.1736292 -0.7892914 NA NA NA 170.8828 154.18994 187.5757 83.62684 75.38473 91.86894
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 6780 4293 0.3340138 -0.0280822 0.6961098 0.0530374 0.0352910 0.0707838 240.9175 209.01236 272.8226 166.97706 134.71308 199.24104
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 4440 2838 0.3125299 -0.1394080 0.7644677 0.0475800 0.0259546 0.0692054 228.2249 194.19666 262.2532 82.58377 66.41175 98.75578
M334 Black Hills Coniferous Forest interior west 716 364 -0.3690625 -1.1087273 0.3706024 0.0314264 -0.0066323 0.0694851 545.1255 -2692.75790 3783.0088 2199.62491 -26186.17339 30585.42321
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 492 287 -1.3327128 -1.8591961 -0.8062295 NA NA NA 233.3563 164.25161 302.4610 159.52952 93.71055 225.34848

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot A (asymptote of B)

## Warning: Removed 6 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 6 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US   0.1625644
## 2       pacific   0.7397534
## 3          east   0.1500463
## 4 interior west  -0.1697212

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.009136160
## 2       pacific  0.030896832
## 3          east  0.001243874
## 4 interior west  0.028079185

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   292.7021
## 2       pacific   524.5473
## 3          east   271.9288
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US  115.02918
## 2       pacific  141.77967
## 3          east   95.14191
## 4 interior west  181.51284